Multi-fidelity sparse polynomial chaos expansion based on Gaussian process regression and least angle regression

Abstract

Polynomial chaos (PC) expansion meta-model has been wildly employed and investigated in the field of uncertainty quantification (UQ) and sensitivity analysis (SA). However, the majority of the multi-fidelity polynomial chaos expansion (MF-PC) models in the literature are still focused on using high-fidelity (HF) PC model to correct low fidelity (LH) model directly, without cross-correlation between PC models of different fidelities. To address this shortcoming, a multi-fidelity sparse polynomial chaos expansion (MF-sPC) model is proposed based on least angle regression (LAR) and recursive Gaussian process regression (GPR) in this paper. From low to high degree of fidelity, the autoregressive scheme in MF GPR is employed to construct MF-sPC model, in which the sparse polynomial chaos (sPC) model of each fidelity is built iteratively coupling with GPR, LAR and cross validation (CV), as gradually expanding the design of experiment (DoE) to reach a given CV error. This recursive scheme finally yields a MF-sPC model with highest fidelity which takes advantage of all sPC models of the lower fidelities. And the proposed MF-sPC model is validated by a test example in detail, and the results reveal that this MF meta-model performs outstanding both in convergence speed and model accuracy.